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318R E F E R E N C E S T O PAR T 225. I . A . Ibragimo v an d R . Z . Khas'minskii , Statistical estimation. Asymptotic theory, "Nauka" ,Moscow, 1 979 ; Englis h transl. , Springer-Verlag , Ne w York-Berlin , 1 981 .26. G . I . Ivchenk o an d Yu . I . Medvedev , Mathematical statistics, "Vysshay a shkola" , Moscow ,1984. (Russian )27. ,Decomposable statistics and hypotheses testing for grouped data, Teor . Veroyatnost .i Primenen . 2 5 (1 980) , no . 3 , 549-560 ; Englis h transl . i n Theor y Probab . Appl . 2 5 (1 981 ) ,no. 3 , 540-551 .28. L . Jaco d an d A . N . Shiryaev , Limit theorems for stochastic processes, 2n d edition , Berlin ,Springer-Verlag, 2003 .29. M . G . Kendal l an d A . Stuart , The advanced theory of statistics. Inference and relationship,vol. 2 , Griffin , London , 1 961 .30. N . Kligen e an d L . Telksnis , Methods of detecting instants of change of random processesproperties, Avtomat . i Telemekh . (1 983) , no . 1 0 , 5-56 ; Englis h transl . i n Automat . Remot eControl 4 4 (1 984) , no . 1 0 , par t 1 , 1 241 -1 283 .31. A . N . Kolmogoro v an d S . V . Fomin , Introductory real analysis, "Nauka" , Moscow , 1 968 ;English t r a n s l , Prentice-Hall , Ne w York , 1 970 .32. A . M . Kolodii , Basics of the general theory of measure and integral, Volgogra d Universit yPress, Volgograd , 1 999 . (Russian )33. S . Kullback , Information theory and statistics, Dover , Ne w York , 1 968 .34. E . L . Lehmann , Theory of point estimation, Wiley , Ne w York , 1 983 .35. F . Lies e an d I . Vajda , Convex statistical distances, Teubner , Leipzig , 1 987 .36. Yu . N . Lin'kov , The asymptotic distinguishability of two simple statistical hypotheses, Pre print 86.45 , Institut e o f Mathematic s o f Ukrainia n Academ y o f Sciences , Kiev , 1 986 .37. ,Asymptotic statistical methods for stochastic processes, "Naukov a dumka" , Kiev ,1993; Englis h transl. , Amer . Math . Soc , Providence , RI , 2001 .38. ,Lectures on mathematical statistics, vol . 1 , "Istoki" , Donetsk , 1 999 ; Englis h transl. ,Part 1 of thi s book .39. ,Large deviation theorems for extended random variables and some applications, J .Math. Sci . 9 3 (1 999) , no . 4 , 563-573 .40. G . V . Martynov , Omega-square tests, "Nauka" , Moscow , 1 978 . (Russian )41. I . P . Natanson , Theory of functions of real variable, GITTL , Moscow , 1 957 ; Englis h transl. ,vol. 1 , Ungar , Ne w York , 1 955 ; vol. 2 , 1 961 .42. J . Neveu , Mathematical foundations of the calculus of probability, Masso n e t Cie , Editeurs ,Paris, 1 964 ; Englis h transl. , Holden-Day , Sa n Francisco-London-Amsterdam , 1 965 .43. C . R . Rao , Statistical inference and its applications, Wiley , Ne w York-London-Sydney, 1 965 .44. R . T . Rockafellar , Convex analysis, Princeto n Univ . Press , Princeton , NJ , 1 970 .45. G . G . Roussas , Contiguity of probability measures: some applications in statistics, Cambridg eUniv. Press , London-Ne w York , 1 972 .46. A . N . Shiryaev , Optimal stopping rules, "Nauka" , Moscow , 1 976 ; Englis h transl. , Springer Verlag, Ne w York-Heidelberg , 1 978 .47. ,Probability, "Nauka" , Moscow , 1 989 ; Englis h transl. , Springer-Verlag , Ne w York ,1996.48. A . V . Skorokhod , Random processes with independent increments, "Nauka" , Moscow , 1 964 ;English transl. , Kluwer , Dordrecht , 1 991 .49. J.-L . Soler , Notion de liberte en statistique mathematique, Thes e d e Docteu r d e Troiseim eCycle, Universit e d e Grenoble , 1 970 . (French )50. F . P . Tarasenko , Nonparametric statistics, Toms k Universit y Press , Tomsk , 1 976 . (Russian )51. A . Wald , Sequential analysis, Wile y an d Chapma n an d Hall , Ne w Yor k an d London , 1 947 .52. A . Wald, Statistical decision functions, Wile y an d Chapma n an d Hall , Ne w York an d London ,1950.53. S . S . Wilks , Mathematical statistics, Wiley , Ne w York-London , 1 967 .54. S . Zacks , The theory of statistical inference, Wiley , Ne w York-London-Sydney , 1 971 .

Indexcr-algebrasufficient, 1 02 , 1 1 6minimal, 1 1 6entropyrelative, 21 8error probability , 20 3of typ e I , 1 59 , 1 86 , 26 3of typ e II , 1 6 0estimatorabsolutely admissible , 4 4admissible, 4 4asymptotically Bayes , 9 6asymptotically efficient , 77 , 8 5in th e stron g (weak ) sense , 7 7asymptotically minimax , 9 7asymptotically R-Bayes , 9 6asymptotically unbiased , 4 0Bayes, 4 5a posteriori , 1 4 2generalized, 4 5consistent, 4 2efficient, 76 , 8 5equivariant, 49 , 5 7likelihood, 1 3 4maximum likelihood , 1 3 4polynomial, 27 3minimax, 1 4 6optimal, 4 4Pitman, 50 , 5 7point, 3 9statistical, 3 9strongly consistent , 4 3superefficient, 9 0unbiased, 4 0excess, 1 2a prior i probability , 1 7 6Bayes approac hcomplete, 1 8 4partial, 1 8 4Bayes estimatio n method , 1 4 3bias (o f th e estimator) , 4 0canonical equation , 3 3conditional expectation , 9 9conditional probability , 1 0 0confidence bounds , 4 0confidence interval , 39 , 1 4 7confidence level , 1 4 7confidence limits , 1 4 7confidence probability , 40 , 1 4 7confidence region , 1 5 0asymptotic, 1 5 0confidence set , 1 9 4uniformly mos t precise , 1 9 6unbiased, 1 9 8convergenceweak, 1 2correlation coefficient , 2 7sampling, 2 9Cramer-Rao bound , 8 8critical set , 26 3decision function , 1 59 , 31 1distancein variance , 20 5Kakutani-Hellinger, 20 6distributionchi-square, 2 1Fisher, 2 4least favorable , 1 7 9Snedekor, 2 4standard normal , 2 0Student, 2 4distribution functio nempirical, 5 , 2 5Kolmogorov, 8 , 26 4families o f hypothese scompletely asymptoticall ydistinguishable, 20 8completely asymptoticall yindistinguishable, 21 1mutually contiguous , 21 5mutually noncontiguous , 21 5family o f function sdense, 21 3uniformly integrable , 21 4319

32 0family o f hypothese scontiguous, 21 3family o f measure scomplete, 1 1 8dominated b y a measure , 1 0 2exponential, 1 2 2relatively compact , 24 8tight, 24 8Fisher information , 62 , 25 7matrix, 8 0Gamma distribution , 1 6Hellinger integral , 20 6hypothesis, 1 5 9composite, 1 5 9main, 26 3null, 26 3one-sided, 1 8 7simple, 1 5 9two-sided, 1 8 7inequalityBarankin-Kiefer, 8 8Bhattacharyya, 8 7Chapman-Robbins, 75 , 8 8Cramer-Rao, 6 8matrix analog , 8 1Kullback-Leibler divergence , 21 8least variance , 3 3lemmaNeyman-Pearson, 1 6 7Stein, 22 3likelihood function , 1 3 3logarithmic, 1 3 3likelihood ratio , 1 6 3location parameter , 4 9mean squar e approximation , 3 2measureabsolutely continuous , 1 6 1measuresequivalent, 1 6 1singular, 1 6 2method o f moments , 1 3 1minimax, 1 7 9mixed moment , 2 6central, 2 6sampling, 2 8sampling, 2 8moment, 8central, 8 , 2 9sampling, 9 , 3 0central, 9 , 3 0INDEXNeyman-Fisher factorizatio n criterion , 1 0 3observation, 1 01 , 1 5 9operating characteristi c (o f a test) , 31 0order (o f th e moment) , 2 9order statistic , 5central, 1 6power function , 1 8 2quantile, 1 6 , 24 0sampling, 1 6random variabl euncorrelated, 2 6random vecto rGaussian, 2 0normal, 2 0random walk , 27 9rank statistic , 28 6reflection method , 27 9regression, 3 1linear, 3 2coefficient of , 3 2sampling, 3 5sampling coefficien t of , 3 5parabolic, 3 4sampling, 3 7regularity condition sCramer-Rao (CR) , 6 1Cramer-Rao (CR)* , 6 9relative stability , 21 9riska posteriori , 1 4 2of th e estimator , 4 5of th e test , 1 9 9risk function , 4 4sample, 2 5sampling space , 3 9scale parameter , 5 6sequenceasymptotically normal , 7Sheppard correction , 27 5skewness, 1 2Spearman ran k correlatio n coefficient , 28 9statistic, 39 , 1 0 1complete, 1 1 8minimal, 1 1 6of th e test , 26 3subordinated, 1 1 6sufficient, 1 0 1statisticsequivalent, 1 1 6stopping rule , 29 3Bayes, 29 4truncated, 29 5

INDEXtestBayes, 1 66 , 1 75 , 1 83 , 31 1chi-square, 27 0empty blocks , 28 5empty boxes , 28 3for independence , 28 8goodness-of-fit, 26 3Kolmogorov, 26 4Pearson, 27 0Smirnov, 28 1symmetric, 28 2Kendall, 29 0likelihood ratio , 20 4Mann-Whitney, 28 7maximum likelihood , 1 67 , 1 8 2minimax, 1 67 , 1 8 4Moran, 29 1Neyman-Pearson, 1 70 , 20 4nonrandomized, 1 59 , 1 7 4of series , 28 6Pearson, 27 3g-Bayes, 31 1quantile, 27 1randomized, 1 59 , 1 7 4rank, 28 6sequential, 29 3Wald, 30 0sign, 27 1Spearman, 28 9statistical, 1 7 4unbiased, 1 9 1uniformly mor e powerful , 1 8 3uniformly mos t powerfu l (UMP) , 1 8 3von Mises-Smirnov , 29 1Wilcoxon, 28 7321theoremGlivenko, 6Kolmogorov, 8 , 26 4Le Cam , first, 25 1Lehmann-SchefTee, 1 2 1Pearson, 26 7Rao-Blackwell-Kolmogorov, 1 1 3trajectory, 27 7Wald identity , 30 4

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Titles i n Thi s Serie s229 Yu . N . Lin'kov , Lecture s i n mathematica l statistics , 200 5228 D . Zhelobenko , Principa l structure s an d method s o f representatio n theory , 200 5227 Takahir o Kawa i an d Y o s h i t s u g u Takei , Algebrai c analysi s o f singula r perturbatio ntheory, 200 5226 V . M . Manuilo v an d E . V . Troitsky , Hilber t C*-modules , 200 5225 S . M . N a t a n z o n , Modul i o f Rieman n surfaces , rea l algebrai c curves , an d thei rsuperanaloges, 200 4224 Ichir o Shigekawa , Stochasti c analysis , 200 4223 M a s a t o s h i N o u m i , Painlev e equation s throug h symmetry , 200 4222 G . G . Magaril-Il'yae v an d V . M . Tikhomirov , Conve x analysis : Theor y an dapplications, 200 3221 K a t s u e i K e n m o t s u , Surface s wit h constan t mea n curvature , 200 3220 I . M . Gelfand , S . G . Gindikin , an d M . I . G r a e v , Selecte d topic s i n integra lgeometry, 200 3219 S . V . Kerov , Asymptoti c representatio n theor y o f th e symmetri c grou p an d it sapplications t o analysis , 200 3218 Kenj i U e n o , Algebrai c geometr y 3 : Furthe r stud y o f schemes , 200 3217 Masak i Kashiwara , D-module s an d microloca l calculus , 200 3216 G . V . B a d a l y a n , Quasipowe r serie s an d quasianalyti c classe s o f functions , 200 2215 Tatsu o Kimura , Introductio n t o prehomogeneou s vecto r spaces , 200 3214 L . S . Grinblat , Algebra s o f set s an d combinatorics , 200 2213 V . N . Sachko v an d V . E . Tarakanov , Combinatoric s o f nonnegativ e matrices , 200 2212 A . V . Mel'nikov , S . N . Volkov , an d M . L . N e c h a e v , Mathematic s o f financialobligations, 200 2211 Take o Ohsawa , Analysi s o f severa l comple x variables , 200 2210 Toshitak e K o h n o , Conforma l field theor y an d topology , 200 2209 Y a s u m a s a Nishiura , Far-from-equilibriu m dynamics , 200 2208 Yuki o M a t s u m o t o , A n introductio n t o Mors e theory , 200 2207 Ken'ich i Ohshika , Discret e groups , 200 2206 Yuj i Shimiz u an d Kenj i U e n o , Advance s i n modul i theory , 200 2205 Seik i Nishikawa , Variationa l problem s i n geometry , 200 1204 A . M . Vinogradov , Cohomologica l analysi s o f partia l differentia l equation s an dSecondary Calculus , 200 1203 T e Su n H a n an d K i n g o Kobayashi , Mathematic s o f informatio n an d coding , 200 2202 V . P . M a s l o v an d G . A . Omel'yanov , Geometri c asymptotic s fo r nonlinea r PDE . I ,2001201 Shigeyuk i Morita , Geometr y o f differentia l forms , 200 1200 V . V . Prasolo v an d V . M . Tikhomirov , Geometry , 200 1199 Shigeyuk i Morita , Geometr y o f characteristi c classes , 200 1198 V . A . Smirnov , Simplicia l an d opera d method s i n algebrai c topology , 200 1197 Kenj i U e n o , Algebrai c geometr y 2 : Sheave s an d cohomology , 200 1196 Y u . N . Lin'kov , Asymptoti c statistica l method s fo r stochasti c processes , 200 1195 M i n o r u W a k i m o t o , Infinite-dimensiona l Li e algebras , 200 1194 Valer y B . N e v z o r o v , Records : Mathematica l theory , 200 1193 Toshi o N i s h i n o , Functio n theor y i n severa l comple x variables , 200 1192 Y u . P . Solovyo v an d E . V . Troitsky , C*-algebra s an d ellipti c operator s i n differentia ltopology, 200 1

TITLES I N THI S SERIE S191190189188Shun-ich i Amar i an d Hirosh i Nagaoka , Method s o f informatio n geometry , 200 0A l e x a n d e r N . Starkov , Dynamica l system s o n homogeneou s spaces , 200 0M i t s u r u Ikawa , Hyperboli c partia l differentia l equation s an d wav e phenomena , 200 0V . V . B u l d y g i n an d Yu . V . Kozachenko , Metri c characterizatio n o f rando m variable sand rando m processes , 200 0187 A . V . Fursikov , Optima l contro l o f distribute d systems . Theor y an d applications , 200 0186 K a z u y a K a t o , N o b u s h i g e Kurokawa , an d Takesh i Saito , Numbe r theor y 1 :Fermat's dream , 200 0185 Kenj i U e n o , Algebrai c Geometr y 1 : Fro m algebrai c varietie s t o schemes , 1 99 9184 A . V . Mel'nikov , Financia l markets , 1 99 9183 H a j i m e S a t o , Algebrai c topology : a n intuitiv e approach , 1 99 9182 I . S . Krasil'shchi k an d A . M . V i n o g r a d o v , Editors , Symmetrie s an d conservatio nlaws fo r differentia l equation s o f mathematica l physics , 1 99 9181 Ya . G . Berkovic h an d E . M . Zhmud' , Character s o f finite groups . Par t 2 , 1 99 9180 A . A . M i l y u t i n an d N . P . Osmolovskii , Calculu s o f variation s an d optima l control ,1998179 V . E . V o s k r e s e n s k i i , Algebrai c group s an d thei r birationa l invariants , 1 99 8178 M i t s u o M o r i m o t o , Analyti c functional s o n th e sphere , 1 99 8177 Sator u Igari , Rea l analysis—wit h a n introductio n t o wavele t theory , 1 99 8176 L . M . Lerma n an d Ya . L . U m a n s k i y , Four-dimensiona l integrabl e Hamiltonia nsystems wit h simpl e singula r point s (topologica l aspects) , 1 99 8175 S . K . G o d u n o v , Moder n aspect s o f linea r algebra , 1 99 8174 Ya-Zh e C h e n an d L a n - C h e n g W u , Secon d orde r ellipti c equation s an d ellipti csystems, 1 99 8173 Yu . A . D a v y d o v , M . A . Lifshits , an d N . V . Smorodina , Loca l propertie s o fdistributions o f stochasti c functionals , 1 99 8172 Ya . G . Berkovic h an d E . M . Zhmud 7 , Character s o f finite groups . Par t 1 , 1 99 8171 E . M . Landis , Secon d orde r equation s o f ellipti c an d paraboli c type , 1 99 8170 V i k t o r P r a s o l o v an d Yur i Solovyev , Ellipti c function s an d ellipti c integrals , 1 99 7169 S . K . G o d u n o v , Ordinar y differentia l equation s wit h constan t coefficient , 1 99 7168 Junjir o N o g u c h i , Introductio n t o comple x analysis , 1 99 8167 M a s a y a Y a m a g u t i , Masayosh i H a t a , an d J u n Kigami , Mathematic s o f fractals , 1 99 7166 Kenj i U e n o , A n introductio n t o algebrai c geometry , 1 99 7165 V . V . Ishkhanov , B . B . Lur'e , an d D . K . Faddeev , Th e embeddin g proble m i nGalois theory , 1 99 7164 E . I . G o r d o n , Nonstandar d method s i n commutativ e harmoni c analysis , 1 99 7163 A . Ya . D o r o g o v t s e v , D . S . Silvestrov , A . V . Skorokhod , an d M . I . Yadrenko ,Probability theory : Collectio n o f problems , 1 99 7162 M . V . B o l d i n , G . I . Simonova , an d Yu . N . Tyurin , Sign-base d method s i n linea rstatistical models , 1 99 7161 Michae l Blank , Discretenes s an d continuit y i n problem s o f chaoti c dynamics , 1 99 7For a complet e lis t o f title s i n thi s series , visi t t h eAMS Bookstor e a t w w w . a m s . o r g / b o o k s t o r e / .

Lectures in mathematica l statistics : part s 1 and 2 / Yu. N. Lin'kov ; translate d by Oleg Klesov and Vladimir Zayats. p. cm. - (Translations of mathematical monographs, ISSN 0065-9282 ; v. 229 ) Includes bibliographical references and index. ISBN -8218-3732-X (alk. paper) 1. Mathematical statistics. I. Title II. Series QA276.16.L5513 2005